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Bifurcation for quasilinear elliptic equations on Rn with natural growth conditions

Published online by Cambridge University Press:  14 November 2011

Cao Daomin ,
Li Gongbao  and
Yan Shusen
Cao Daomin
Affiliation:
Wuhan Institute of Mathematical Sciences, Academia Sinica, P.O. Box 30, Wuhan 430071, P. R. China
Li Gongbao
Affiliation:
Wuhan Institute of Mathematical Sciences, Academia Sinica, P.O. Box 30, Wuhan 430071, P. R. China
Yan Shusen
Affiliation:
Wuhan Institute of Mathematical Sciences, Academia Sinica, P.O. Box 30, Wuhan 430071, P. R. China
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Synopsis

We consider the following eigenvalue problem:

We prove the existence of H1(Rn)∩L∞(Rn) bifurcation at λ=0 but only require aij(x, t) (i,j= 1, 2, …,n) and f(x, t) to satisfy certain conditions in theneighbourhood of Rn × {0}.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 113 , Issue 3-4 , 1989 , pp. 215 - 228
Copyright
Copyright © Royal Society of Edinburgh 1989

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